Warm oil in a large saucepan over medium-high heat. Add celery, tomatoes and oregano and cook, stirring occasionally, until celery begins to soften, about 3 minutes. Add garlic and sauté until fragrant, 2 minutes longer.
Stir in broth and bring soup to a boil. Carefully add tortellini and beans and cook, stirring occasionally, until soup is heated through and tortellini are tender, about 7 minutes. Season with salt, if desired. Divide soup among 4 bowls, sprinkle each with 1 Tbsp. Parmesan and serve immediately.